Susan,
Your family history about the Orr family sounds correct. The counties of Ulster were very heavily settled by Scots who mostly arrived in the 1600s. Something like 200,000 Scots moved to Ireland then representing about 15% of the entire Scottish population. Many were dis-satisfied with life in Ireland and decided to move on again in the 1700s, mainly to North America. (In contrast, “native Irish” did not start migrating in significant numbers till the 1800s).
You haven’t said what denomination the Orrs were but most probably they were Presbyterian. So where you have someone who left Ireland in the 1700s, lived in Ulster, had a Scottish surname and was Presbyterian you have 4 separate pointers to them being of Scottish origins. In North America they tend to be called Scotch-Irish. In Ireland it’s Ulster Scots.
I looked at the 1901 Irish census. There were 3052 people named Orr. Almost all were Protestant, either Presbyterian or Church of Ireland. So all descended from settlers from Scotland or perhaps England. Here’s a link to the Ulster-Scots Agency website which contains general information about your ancestors. There’s still a lot of interest in the subject to this day:
https://www.ulsterscotsagency.com
That said, it’s almost impossible to research someone who left Ireland in the 1700s. The records just don’t exist. Only a handful of the many Presbyterian churches kept records in the 1700s, and there’s no easy way around that. Even if we knew exactly where your family originated, there’s probably no documentary record of them in that place, unless they were very wealthy or notorious in some way.
A famous Orr got hanged in 1797, on the basis of probably false evidence, so we know a little about him. He is remembered now as a hero with the by-line of “Remember Orr.”
https://en.wikipedia.org/wiki/William_Orr_(United_Irishman)
I would say that you have to hope that someone else will be able to link to your family through a greater knowledge of the family background. Or possibly you might make a link using DNA.
